Well if you wan a really early start you can join a drag racing league called JDRL (Junior Dragster Racing leage) like my self. You have to be at least 8 years of age and can race until the age of 16. And after 16 you can move up to big cars.
In the U.S. it can vary from state to state and even sanction to sanction, I have heard, with parents consent, age 16. There may be some other considerations involved also.